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What Is The Area of A Circle?

A one is not a square, but a circle"s area (the lot of interior room enclosed by the circle) is measured in square units. Finding the area that a square is easy: size times width.

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A circle, though, has actually only a diameter, or distance across. It has actually no clearly visible length and also width, due to the fact that a circle (by definition) is the set of all points equidistant from a given point at the center.

Yet, with just the diameter, or half the diameter (the radius), or also only the circumference (the distance around), you deserve to calculate the area of any kind of circle.

How To uncover The Area that A Circle

Recall the the relationship in between the one of a circle and its diameter is always the exact same ratio, 3.14159265, pi, or π. That number, π, time the square the the circle"s radius gives you the area that the within of the circle, in square units.

Area the A one Formula

If you know the radius, r, in every little thing measurement devices (mm, cm, m, inches, feet, and also so on), usage the formula π r2 to uncover area, A:

The answer will be square devices of the linear units, such together mm2, cm2, m2, square inches, square feet, and also so on.

Here is a circle with a radius that 7 meters. What is the area?

A = π·r2

A = π × 72

A = π × 49

A = 153.9380 m2

Area the A Circle making use of Diameter

If you know the diameter, d, in every little thing measurement units, take fifty percent the diameter to gain the radius, r, in the exact same units.

Here is the actual estate breakthrough of sun City, Arizona, a circular town with a diameter that 1.07 kilometers. What is the area of sunlight City?


First, find fifty percent the diameter, given, to obtain the radius:

1.072 = 0.535 km = 535 m

Plug in the radius right into our formula:

A = π·r2

A = π × 5352

A = π × 286,225

A = 899,202.3572 m2

To transform square meters, m2, to square kilometers, km2, division by 1,000,000:

A = 0.8992 km2

Sun City"s westernmost one housing advancement has one area of practically 1 square kilometer!

How to calculate the Area that a Circle

Try this area calculations because that four different circles. It is in careful; some offer the radius, r, and some offer the diameter, d.

Remember come take half the diameter to find the radius prior to squaring the radius and also multiplying by π.


A 406-mm bicycle wheelThe London Eye Ferris wheel with a radius of 60 metersA 26-inch bicycle wheelThe world"s biggest pizza had a radius that 61 feet, 4 customs (736 inches)


A 406-mm bicycle wheel has a radius, r, the 203 mm:

A = πr2

A = π × 203 mm2

A = 637.7433 mm2

The London Eye Ferris wheel"s 60-meter radius:

A = πr2

A = π × 60 m2

A = 188.4955 m2

A 26-inch bicycle wheel has actually a radius, r, that 13 inches:

A = πr2

A = π × 13 in2

A = 530.9291 in2

The world"s largest pizza through its 736-inch radius:

A = πr2

A = π × 736 in2

A = 1,701,788.17 in2

That is 11,817.97 ft2 of pizza! Yum! Anyway, just how did you execute on the 4 problems?

Area the A Circle utilizing Circumference

If you have no idea what the radius or diameter is, but you understand the circumference of the circle, C, you can still uncover the area.

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Area and Circumference Formula

Circumference (the distance roughly the circle) is discovered with this formula:

C = 2πr

That way we have the right to take the one formula and also "solve because that r," which offers us:

r = C2π

We can replace r in our initial formula through that new expression:

A = π C2π2

That expression simplifies come this:

That formula works every time!

How To discover The Area with Circumference

Here is a beautiful, reasonable-sized pizza you and three friends have the right to share. You happen to understand the circumference of your pizza is 50.2655 inches, but you do not understand its complete area. You desire to know how many square inch of pizza you will certainly each enjoy.

Substitute 50.2655 inches because that C in the formula:

A = 50.265524π

A = 2,526.62044π

A = 201.0620 in2

Equally division that full area for a full-sized pizza amongst four friends, and also you each obtain 50.2655 in2 that pizza! That"s about a 3rd of a square foot because that each of you! Yum, yum!